The subject matter of this specification relates to a new finite volume method (and associated system and program storage device) for a set of Linear Elasticity equations described below; and, in particular, to a finite volume approach to discretization of a set of equations of Linear Elasticity on a general unstructured grid in three dimensions.
The flow equations in commercial reservoir simulators are generally discretized using the finite difference or finite volume method, whereas for stress equations it is more common to use the finite element approach. In a reservoir simulator designed to include geomechanical effects, these two distinct types of equations must be solved with some degree of coupling. It is therefore natural to ask: whether suitable finite volume methods can be derived for the stress equations so that the stress and fluid flow models can share a common derivation, and what the relative merits of finite volume and finite element methods are for these coupled systems.
In this specification, a finite volume discretization of a set of stress equations, as implemented in a commercial reservoir simulator, is presented with an option to couple the stress with the fluid flow. The method, as presented, is locally conservative and retains second order accuracy on general three-dimensional grids. The imposition of various types of boundary conditions is discussed and the implementation of special features is described, such as faults, pinch-outs and local grid refinements. A comparison with other approaches is presented based on finite differences (see References 1 and 2 below) and finite elements (see Reference 3 below). The relative accuracy, efficiency and robustness of these three different approaches are also discussed.